CN107070278A - A kind of discontinuous pulse duration modulation method of three-level current transformer neutral-point potential balance - Google Patents

A kind of discontinuous pulse duration modulation method of three-level current transformer neutral-point potential balance Download PDF

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CN107070278A
CN107070278A CN201710496361.3A CN201710496361A CN107070278A CN 107070278 A CN107070278 A CN 107070278A CN 201710496361 A CN201710496361 A CN 201710496361A CN 107070278 A CN107070278 A CN 107070278A
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msub
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max
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CN107070278B (en
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姜卫东
王磊
张学威
王金平
皋艳
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Zhongke Haiao Mount Huangshan Energy Storage Technology Co ltd
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Hefei University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483—Converters with outputs that each can have more than two voltages levels
    • H02M7/487—Neutral point clamped inverters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • H02M7/539—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters with automatic control of output wave form or frequency
    • H02M7/5395—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters with automatic control of output wave form or frequency by pulse-width modulation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/0048—Circuits or arrangements for reducing losses
    • H02M1/0054—Transistor switching losses
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/10—Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)
  • Inverter Devices (AREA)

Abstract

The invention discloses a kind of discontinuous pulse duration modulation method of three-level current transformer neutral-point potential balance, including：1st, capacitance voltage, three-phase output voltage, three-phase current above and below collection three-level current transformer DC side；2nd, the magnitude relationship of three-level current transformer three-phase output voltage is compared；3rd, the midpoint electric current under different clamper modes is calculated；4th, the midpoint electric current obtained according to instantaneous midpoint potential, modulation degree and calculating selects suitable clamper mode to control midpoint potential；5th, according to selected clamper mode, corresponding carrier mode is selected, threephase switch sequence is obtained.The present invention can effectively control the midpoint potential of three-level current transformer, reduce the switching loss of power device, so as to realize the optimal control of three-level current transformer.

Description

A kind of discontinuous pulse duration modulation method of three-level current transformer neutral-point potential balance
Technical field
The present invention relates to the control method of three-level current transformer, more particularly to a kind of three-level current transformer midpoint The discontinuous pulse duration modulation method of potential balance.
Background technology
With the development of Power Electronic Technique, especially in Large Copacity, high voltage occasion, the application of three-level topology is increasingly Extensively, the voltage that each power tube is born is the half of DC voltage.In addition, three-level topology is also humorous with output waveform Ripple content is low, efficiency high advantage.But due to increasing for power tube quantity, control algolithm is complicated, along with mid-point potential offset The problems such as.
In order that three-level inverter safe and reliable operation, it is necessary to ensure that midpoint potential is the half of DC voltage.Often The method for the balance midpoint potential seen mainly has following 3 kinds：
1) injected with extra current transformer to electric capacity midpoint or extract electric current；
2) capacitance voltage is derived from the dc source of two-way independence up and down；
3) midpoint potential is balanced by adjusting width-modulation pulse sequence.Wherein, increase hardware can increase system cost； Cost will not be increased by changing algorithm, thus most attractive.
The algorithm of conventional neutral-point potential balance mainly has two kinds at present：The carried based PWM injected based on zero-sequence component (CBPWM) method and space vector modulation (SVPWM) method adjusted based on redundant vectors.Residual voltage in carrier modulating method Calculating, complexity of Vector modulation rule etc. causes the computation complexity of control algolithm significantly in space vector modulating method Lifting.In addition, above two modulator approach is set up above and below DC side on the basis of electric capacity voltage symmetry, if there is DC side Asymmetrical voltage, unbalanced situation, capacitance voltage is no longer the half of DC voltage up and down, and three traditional level methods will No longer it is applicable.
Further, since the raising of power tube switching frequency, the switching loss of power tube is consequently increased.In power converter system In system, device loss (including conduction loss and switching loss) is the influence vital ring of system effectiveness.It is existing to reduce The method of switching loss is broadly divided into three classes：
(1) voltage or electric current (soft switch technique) on the interval interior switch of commutation are reduced；
(2) period of switching time is changed；
(3) modulation system is changed.
Using soft switch technique, it can effectively reduce the switching loss of power tube, but the application of Sofe Switch can be added to This, control is complicated, and is limited during modulation by stage.The switching loss of current transformer has very high point with specific modulation system System, switching loss can be reduced to a certain extent by improving modulation system.
Accordingly, it is desirable to provide a kind of three-level current transformer of reduction system switching loss while realize neutral-point potential balance Modulator approach.
The content of the invention
The present invention is that, in order to solve the weak point that above-mentioned prior art is present, a kind of three-level current transformer midpoint of proposition is electric The discontinuous pulse duration modulation method of position balance, to can effectively suppress midpoint potential ripple under different capacity factor, modulation degree It is dynamic, the output harmonic wave of three-level current transformer is reduced, so as to realize the optimal control of three-level current transformer.
In order to solve the above-mentioned technical problem, the present invention is adopted the following technical scheme that：
A kind of the characteristics of discontinuous pulse duration modulation method of three-level current transformer neutral-point potential balance of the present invention, is by following step It is rapid to carry out：
Step 1, gathered respectively above and below the DC side of the three-level current transformer using voltage sensor and current sensor Capacitance voltage uC1,uC2, three-phase output voltage uA、uB、uCWith three-phase current iA、iB、iC；
Step 2, the output three-phase voltage u using the relatively more described three-level current transformer of formula (1)A、uB、uCSize, obtain institute State the output three-phase voltage u of three-level current transformerA、uB、uCMiddle maximum voltage umax, minimum voltage uminWith medium voltage umid：
By the maximum voltage u in formula (1)maxCorresponding phase, is designated as umaxPhase；Minimum voltage uminCorresponding phase, is designated as uminPhase, medium voltage umidCorresponding phase, is designated as umidPhase；
Step 3, according to modulation degree m by umaxPositive bus-bar or center line are mutually clamped to, by uminMutually it is clamped to negative busbar or center line； Work as m>When 0.5, according to formula (2) by umaxPositive bus-bar is mutually clamped to, and is designated as DPWM_max clamper modes, so as to obtain such as formula (4) Midpoint electric current i under shown DPWM_max clamper modes0,max；According to formula (3) by uminNegative busbar is mutually clamped to, and is designated as DPWM_min clamper modes, so as to obtain the midpoint electric current i under the DPWM_min clamper modes as shown in formula (5)0,min：
ucom=udc/2-umax
ucom=-udc/2-umin
In formula (2) and formula (3), u 'max,u′mid,u′minThe three-level current transformer injection common-mode voltage u is represented respectivelycom Modulation voltage afterwards；In formula (4) and formula (5), p represents the power output of the three-level current transformer, and has：P=uAiA+uBiB+ uCiC=uA′iA+uB′iB+uC′iC；udcFor current transformer DC voltage, and have：udc=uC1+uC2；uC1Represent electric capacity on DC side Voltage, uC2Represent capacitance voltage under DC side；
Step 4, work as m<When 0.5, according to formula (6) by uminCenter line is mutually clamped to, and is designated as DPWM_mid1 clamper modes, from And obtain the midpoint electric current i under the DPWM_mid1 clamper modes as shown in formula (8)0,mid1；According to formula (7) by umaxMutually it is clamped to Center line, and DPWM_mid2 clamper modes are designated as, so as to obtain the midpoint electricity under the DPWM_mid2 clamper modes as shown in formula (9) Flow i0,mid2：
ucom=-umax
ucom=-umin
Step 5, according to capacitance voltage u above and below modulation degree m, DC sideC1,uC2And formula (4), formula (5), formula (8), formula (9) Calculate obtained i0,max、i0,min、i0,mid1And i0,mid2, according to selection principle be chosen so that above and below capacitor voltage balance pincers Position mode；The selection principle is：
If uC1＞ uC2, then select to make the elevated clamper mode of midpoint potential, i.e. selection calculate obtained i0,max、i0,min、 i0,mid1And i0,mid2Clamper mode corresponding to middle maximum；If conversely, uC1＜ uC2, then the pincers for reducing midpoint potential are selected Position mode, i.e. selection calculate obtained i0,max、i0,min、i0,mid1And i0,mid2Clamper mode corresponding to middle minimum value；
Step 6, according to selected clamper mode, select corresponding carrier mode, and calculate threephase switch sequence, from And realize the control to the three-level current transformer.
Compared with the modulator approach of traditional three-level current transformer, beneficial effects of the present invention are embodied in：
1. the present invention is according to instantaneous midpoint potential, judging to use makes the clamper mode that midpoint potential is raised and lowered, root Corresponding midpoint electric current under the different clamper modes obtained according to calculating, selection midpoint current maxima or the corresponding clamper of minimum value Mode, makes midpoint potential gradually balance, and effectively inhibits Neutral-point Potential Fluctuation, so as to obtain preferable harmonic characterisitic and control Effect.
2. it is of the invention compared with traditional modulator approach, without the accurate work for calculating residual voltage or each redundant vectors of distribution With the time, it is only necessary to which the voltage and current signal obtained according to real-time sampling calculates the midpoint electric current under each clamper mode, and root According to instantaneous midpoint potential, selection makes the clamper mode that midpoint potential is raised and lowered, so as to reduce algorithm to a certain extent Computational complexity；
3. the present invention is always ensured that switch motion does not occur for a certain phase bridge arm of three-level current transformer in controlling cycle, so that Reduce the switching loss of current transformer, the operational efficiency of the current transformer of raising；
4. the present invention need not increase any peripheral hardware, system cost is low, and control method is simple, it is easy to accomplish.
Brief description of the drawings
Fig. 1 is the main circuit diagram of NPC three-level converter in the prior art；
Fig. 2 is existing carrier mode figure；
Fig. 3 is the midpoint map of current that three-level current transformer of the present invention is operated under situation；
Fig. 4 is inventive control algorithm flow chart；
Fig. 5 a are the Steady Experimental result figure that three-level current transformer of the present invention is operated under m=0.4, pf=0.94 situations；
Fig. 5 b are the Steady Experimental result figure that three-level current transformer of the present invention is operated under m=0.4, pf=0.17 situations；
Fig. 5 c are the Steady Experimental result figure that three-level current transformer of the present invention is operated under m=0.8, pf=0.94 situations；
Fig. 5 d are the Steady Experimental result figure that three-level current transformer of the present invention is operated under m=0.8, pf=0.17 situations；
Fig. 6 a are the Dynamic experimental results figure that three-level current transformer of the present invention is operated under m=0.4, pf=0.94 situations；
Fig. 6 b are the Dynamic experimental results figure that three-level current transformer of the present invention is operated under m=0.4, pf=0.17 situations；
Fig. 6 c are the Dynamic experimental results figure that three-level current transformer of the present invention is operated under m=0.8, pf=0.94 situations；
Fig. 6 d are the Dynamic experimental results figure that three-level current transformer of the present invention is operated under m=0.8, pf=0.17 situations.
Embodiment
In the present embodiment, a kind of discontinuous pulse duration modulation method of three-level current transformer neutral-point potential balance is real-time detection Capacitance voltage, phase voltage, phase current above and below DC side, and judge the magnitude relationship of three-phase output voltage.According to electric capacity electricity up and down The suitable clamper mode of selection of differential pressure and carrier mode, inject corresponding common-mode voltage, and then obtain corresponding on off sequence, tool Body is said, as shown in Fig. 2 be to carry out as follows：
Step 1, utilize voltage sensor and current sensor collection three-level current transformer DC side above and below capacitance voltage uC1,uC2, three-phase output voltage uA、uB、uC, three-phase current iA、iB、iC；
Δ u defined in specific implementationc=uC1-uC2For electric capacity voltage difference up and down.As shown in figure 1, entering in three-level current transformer During row modulation, current transformer A, B, C three-phase inevitably extract electric current or to midpoint Injection Current from midpoint, cause midpoint potential Shift or fluctuate, current transformer is even resulted in when serious normally to be run.To ensure the stable safety fortune of three-level current transformer OK, neutral-point potential balance need to be controlled, electric capacity voltage difference meets Δ u up and downc=0.
Step 2, the output three-phase voltage u using the relatively more described three-level current transformer of formula (1)A、uB、uCSize, obtain three The output three-phase voltage u of level current transformerA、uB、uCMiddle maximum voltage umax, minimum voltage uminWith medium voltage umid；Wherein, Maximum voltage umaxCorresponding phase, is designated as umaxPhase；Minimum voltage uminCorresponding phase, is designated as uminPhase；And medium voltage umidCorresponding phase, is designated as umidPhase；
Step 3, according to modulation degree m by umaxPositive bus-bar or center line are mutually clamped to, by uminMutually it is clamped to negative busbar or center line； Work as m>When 0.5, according to formula (2) by umaxPositive bus-bar is mutually clamped to, and is designated as DPWM_max clamper modes, so as to obtain such as formula (4) Midpoint electric current i under shown DPWM_max clamper modes0,max；According to formula (3) by uminNegative busbar is mutually clamped to, and is designated as DPWM_min clamper modes, so as to obtain the midpoint electric current i under the DPWM_min clamper modes as shown in formula (5)0,min：
ucom=udc/2-umax
ucom=-udc/2-umin
In formula (2), (3), u 'max,u′mid,u′minThe three-level current transformer injection common-mode voltage u is represented respectivelycomAfterwards Modulation voltage；In formula (4), (5), p represents the power output of the three-level current transformer, and p=uAiA+uBiB+uCiC=uA′iA+ uB′iB+uC′iC；udcFor current transformer DC voltage, and there is udc=uC1+uC2；uC1Represent capacitance voltage, u on DC sideC2Represent Capacitance voltage under DC side；
Step 4, work as m<When 0.5, according to formula (6) by uminCenter line is mutually clamped to, and is designated as DPWM_mid1 clamper modes, from And obtain the midpoint electric current i under the DPWM_mid1 clamper modes as shown in formula (8)0,mid1；According to formula (7) by umaxMutually it is clamped to Center line, and DPWM_mid2 clamper modes are designated as, so as to obtain the midpoint electricity under the DPWM_mid2 clamper modes as shown in formula (9) Flow i0,mid2：
ucom=-umax
ucom=-umin
Step 5, according to capacitance voltage u above and below modulation degree m, DC sideC1,uC2And by formula (4), formula (5), formula (8), Formula (9) calculates obtained i0,max、i0,min、i0,mid1And i0,mid2, according to selection principle be chosen so that above and below capacitor voltage balance Clamper mode；The selection principle is：
If uC1＞ uC2, should be selected such that the elevated clamper mode of midpoint potential, i.e. selection calculate obtained i0,max、i0,min、 i0,mid1And i0,mid2The corresponding clamper mode of middle maximum；If conversely, uC1＜ uC2, should be selected such that the clamper of midpoint potential reduction Mode, i.e. selection calculate obtained i0,max、i0,min、i0,mid1And i0,mid2The corresponding clamper mode of middle minimum value；
In embodiment：With m=0.9,Exemplified by, the influence of the midpoint electric current alignment current potential obtained to calculating is entered Row is described in detail：Wherein midpoint electric current with three times sinusoidal frequency repeat, to ω t ∈ (0,2 π/3) illustrate, ω t ∈ (2 π/3, 2 π) it is similar.
As shown in figure 3, according to i0, max、i0, minChange in polarity rule by the operative condition of midpoint electric current alignment current potential It is divided into following five stages.When defining midpoint electric current more than 0, current transformer is declined by midpoint output current, midpoint potential；Midpoint electricity When stream is less than 0, current transformer is raised to midpoint Injection Current, midpoint potential.The 1st, 3 in Fig. 3, in 5 stages, i0, max＞ 0, i0, min ＜ 0, represents to raise midpoint potential using DPWM_max methods, and reduces midpoint potential using DPWM_min methods；2nd rank Duan Zhong, i0, max＜ 0, i0, min＜ 0, represents no matter use DPWM_max, or DPWM_min methods, and midpoint potential is reduced all the time, Due to | i0,min| ＜ | i0,max|, less Neutral-point Potential Fluctuation can be obtained using DPWM_min methods；In 4th stage, i0, max ＞ 0, i0, min＞ 0, represents no matter use DPWM_max, or DPWM_min methods, and midpoint potential is raised all the time, due to | i0,min | ＞ | i0,max|, less Neutral-point Potential Fluctuation can be obtained using DPWM_max methods；
Step 6, according to selected clamper mode, select corresponding carrier mode, and calculate threephase switch sequence, from And realize the control to the three-level current transformer.
In specific implementation, control flow of the invention is calculated as shown in figure 4, first, it is determined that the relation of three-phase voltage Midpoint electric current under various clamper modes；Secondly, according to electric capacity voltage difference above and below the DC side detected in real time, the suitable pincers of selection Position mode；Finally, the carrier mode generation threephase switch sequence according to table 1, realizes modulation.
Table 1 is the corresponding carrier mode table of the different clamper modes of the present invention
In embodiment：Different modulation degree m is chosen respectively and power factor pf is tested, and verifies modulation methods of the present invention The correctness of method, whereinU is output line voltage peak value, u 'A,u′B,u′CThe modulation respectively obtained using the present invention Voltage, uABThe line voltage waveform obtained for the present invention.
Comparison diagram 5a, Fig. 6 a；Fig. 5 b, Fig. 6 b；Fig. 5 c, Fig. 6 c are understood, in m=0.4, pf=0.94；M=0.4, pf= 0.17；When m=0.8, pf=0.94, no matter electric capacity whether there is initial voltage difference above and below DC side, all the time can using the present invention Midpoint potential is enough rebalanced, i.e., in the absence of obvious direct current offset and AC ripple.In addition, the output electricity of three-level current transformer Flow sine degree preferable.
Comparison diagram 5d, Fig. 6 d are understood, in m=0.8, pf=0.17, and no matter electric capacity is with the presence or absence of initial above and below DC side Voltage difference, can effectively control midpoint potential using the present invention, in the absence of obvious direct current offset, but there is less frequency tripling Fluctuation.In addition, the output current sine degree of three-level current transformer is preferable.

Claims (1)

1. a kind of discontinuous pulse duration modulation method of three-level current transformer neutral-point potential balance, its feature is carried out as follows：
Step 1, using voltage sensor and current sensor electric capacity above and below the DC side of the three-level current transformer is gathered respectively Voltage uC1,uC2, three-phase output voltage uA、uB、uCWith three-phase current iA、iB、iC；
Step 2, the output three-phase voltage u using the relatively more described three-level current transformer of formula (1)A、uB、uCSize, obtain described three The output three-phase voltage u of level current transformerA、uB、uCMiddle maximum voltage umax, minimum voltage uminWith medium voltage umid：
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By the maximum voltage u in formula (1)maxCorresponding phase, is designated as umaxPhase；Minimum voltage uminCorresponding phase, is designated as umin Phase, medium voltage umidCorresponding phase, is designated as umidPhase；
Step 3, according to modulation degree m by umaxPositive bus-bar or center line are mutually clamped to, by uminMutually it is clamped to negative busbar or center line；Work as m> When 0.5, according to formula (2) by umaxPositive bus-bar is mutually clamped to, and is designated as DPWM_max clamper modes, so as to obtain as shown in formula (4) DPWM_max clamper modes under midpoint electric current i0,max；According to formula (3) by uminNegative busbar is mutually clamped to, and is designated as DPWM_ Min clamper modes, so as to obtain the midpoint electric current i under the DPWM_min clamper modes as shown in formula (5)0,min：
ucom=udc/2-umax
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mi>max</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mi>max</mi> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>u</mi> <mi>max</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mi>min</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mi>min</mi> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> <mo>+</mo> <msub> <mi>u</mi> <mi>min</mi> </msub> <mo>-</mo> <msub> <mi>u</mi> <mi>max</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
ucom=-udc/2-umin
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mi>max</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mi>max</mi> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> <mo>+</mo> <msub> <mi>u</mi> <mi>max</mi> </msub> <mo>-</mo> <msub> <mi>u</mi> <mi>min</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>u</mi> <mi>min</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mi>min</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mi>min</mi> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>i</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>max</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <mfrac> <mrow> <mn>2</mn> <mi>p</mi> </mrow> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> </mfrac> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>u</mi> <mi>max</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> <mo>,</mo> <msubsup> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>&gt;</mo> <msubsup> <mi>u</mi> <mi>min</mi> <mo>&amp;prime;</mo> </msubsup> <mo>&gt;</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mn>2</mn> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> </mfrac> <mrow> <mo>(</mo> <mo>-</mo> <mi>p</mi> <mo>+</mo> <mn>2</mn> <msubsup> <mi>u</mi> <mi>min</mi> <mo>&amp;prime;</mo> </msubsup> <msub> <mi>i</mi> <mi>min</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>u</mi> <mi>max</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> <mo>,</mo> <msubsup> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>&gt;</mo> <mn>0</mn> <mo>&gt;</mo> <msubsup> <mi>u</mi> <mi>min</mi> <mo>&amp;prime;</mo> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mn>2</mn> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> </mfrac> <mrow> <mo>(</mo> <mi>p</mi> <mo>-</mo> <mn>2</mn> <msubsup> <mi>u</mi> <mi>max</mi> <mo>&amp;prime;</mo> </msubsup> <msub> <mi>i</mi> <mi>max</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>u</mi> <mi>max</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mn>0</mn> <mo>&gt;</mo> <msubsup> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>&gt;</mo> <msubsup> <mi>u</mi> <mi>min</mi> <mo>&amp;prime;</mo> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>i</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>min</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mfrac> <mrow> <mn>2</mn> <mi>p</mi> </mrow> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mrow> <mn>0</mn> <mo>&gt;</mo> <msubsup> <mi>u</mi> <mi>max</mi> <mo>&amp;prime;</mo> </msubsup> <mo>&gt;</mo> <msubsup> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>u</mi> <mi>min</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mn>2</mn> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> </mfrac> <mrow> <mo>(</mo> <mi>p</mi> <mo>-</mo> <mn>2</mn> <msubsup> <mi>u</mi> <mi>max</mi> <mo>&amp;prime;</mo> </msubsup> <msub> <mi>i</mi> <mi>max</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>u</mi> <mi>max</mi> <mo>&amp;prime;</mo> </msubsup> <mo>&gt;</mo> <mn>0</mn> <mo>&gt;</mo> <msubsup> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>,</mo> <msubsup> <mi>u</mi> <mi>min</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mn>2</mn> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> </mfrac> <mrow> <mo>(</mo> <mo>-</mo> <mi>p</mi> <mo>+</mo> <mn>2</mn> <msubsup> <mi>u</mi> <mi>min</mi> <mo>&amp;prime;</mo> </msubsup> <msub> <mi>i</mi> <mi>min</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>u</mi> <mi>max</mi> <mo>&amp;prime;</mo> </msubsup> <mo>&gt;</mo> <msubsup> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>&gt;</mo> <mn>0</mn> <mo>,</mo> <msubsup> <mi>u</mi> <mi>min</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
In formula (2) and formula (3), u 'max,u′mid,u′minThe three-level current transformer injection common-mode voltage u is represented respectivelycomAfterwards Modulation voltage；In formula (4) and formula (5), p represents the power output of the three-level current transformer, and has：P=uAiA+uBiB+uCiC =uA′iA+uB′iB+uC′iC；udcFor current transformer DC voltage, and have：udc=uC1+uC2；uC1Represent electric capacity electricity on DC side Pressure, uC2Represent capacitance voltage under DC side；
Step 4, work as m<When 0.5, according to formula (6) by uminCenter line is mutually clamped to, and is designated as DPWM_mid1 clamper modes, so as to obtain Obtain the midpoint electric current i under the DPWM_mid1 clamper modes as shown in formula (8)0,mid1；According to formula (7) by umaxCenter line is mutually clamped to, And DPWM_mid2 clamper modes are designated as, so as to obtain the midpoint electric current under the DPWM_mid2 clamper modes as shown in formula (9) i0,mid2：
ucom=-umax
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mi>max</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mi>max</mi> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>u</mi> <mi>max</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mi>min</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mi>min</mi> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>u</mi> <mi>min</mi> </msub> <mo>-</mo> <msub> <mi>u</mi> <mi>max</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
ucom=-umin
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mi>max</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mi>max</mi> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>u</mi> <mi>max</mi> </msub> <mo>-</mo> <msub> <mi>u</mi> <mi>min</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>u</mi> <mi>min</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>u</mi> <mi>min</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msub> <mi>u</mi> <mi>min</mi> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>i</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>m</mi> <mi>i</mi> <mi>d</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>p</mi> </mrow> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>i</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>m</mi> <mi>i</mi> <mi>d</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mn>2</mn> <mi>p</mi> </mrow> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
Step 5, according to capacitance voltage u above and below modulation degree m, DC sideC1,uC2And formula (4), formula (5), formula (8), formula (9) are calculated Obtained i0,max、i0,min、i0,mid1And i0,mid2, according to selection principle be chosen so that above and below capacitor voltage balance clamper side Formula；The selection principle is：
If uC1＞ uC2, then select to make the elevated clamper mode of midpoint potential, i.e. selection calculate obtained i0,max、i0,min、i0,mid1 And i0,mid2Clamper mode corresponding to middle maximum；If conversely, uC1＜ uC2, then the clamper side for reducing midpoint potential is selected Formula, i.e. selection calculate obtained i0,max、i0,min、i0,mid1And i0,mid2Clamper mode corresponding to middle minimum value；
Step 6, according to selected clamper mode, corresponding carrier mode is selected, and calculate threephase switch sequence, so that real Now to the control of the three-level current transformer.
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CN111064377A (en) * 2019-11-28 2020-04-24 中国科学院电工研究所 Synchronous carrier DPWM method for avoiding two-level jump of phase voltage of three-level inverter
CN111953223A (en) * 2020-08-12 2020-11-17 合肥工业大学 Neutral point voltage balancing method for three-phase four-wire system three-level converter
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CN112421977A (en) * 2020-09-30 2021-02-26 南洋电力设备有限公司 Independent capacitor voltage control method of three-level converter
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CN116032144A (en) * 2023-03-29 2023-04-28 成都希望电子研究所有限公司 Synchronous overmodulation algorithm for cooperative control of harmonic wave and midpoint potential
CN117240060A (en) * 2023-11-15 2023-12-15 特变电工西安电气科技有限公司 Method, device, converter and system for coping with midpoint bias voltage of low modulation degree
CN117240060B (en) * 2023-11-15 2024-03-12 特变电工西安电气科技有限公司 Method, device, converter and system for coping with midpoint bias voltage of low modulation degree

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